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166         ON THE COLOURS OF THICK PLATES.
mirror equal to that of coincident conjugate foci.    This agrees with observation*.
Whatever be the position of the luminous point, if a!, &', c' be the co-ordinates of its image, we have
!                        and the second line in the expression for AJ? becomes
2* A     1
 -+
fiJLC \C       C
'}|j|    i                        which vanishes since c' satisfies the second of equations (12).    If a
I                        screen be held in a direction perpendicular to the axis of the
!                        mirror, at such a distance as to receive a distinct image of the
                        luminous point, and if a', V, c' be now taken to denote the co-
1                      ordinates, not of the image itself, but of a point of the screen very
i                        near the image, the part of AJS which involves the squares of x
and y will continue to vanish, inasmuch as cf remains the same as before, and the part which contains first powers, though not absolutely evanescent, will be very small; and therefore a portion of the system of rings in the neighbourhood of the image will be formed distinctly.
5. This agrees with observation. In repeating Newton's experiment in his way, except that a lens of short focus was employed instead of a small hole, and that the surface of the glass was purposely dimmed with milk and water, I found that when the mirror was placed at a distance from the luminous point widely different from its radius of curvature, and inclined a little, so as to allow of receiving the image on a sheet of paper without stopping the incident light, and when the paper was held at such a distance from the mirror as to receive a distinct image of the luminous point, the image was accompanied by very'distinct arcs of rings.
* See Newton's Optics, Book II., Part iv., Obs. 1, for the case in which the curvatures of the two surfaces are alike, and an experiment by the Duke de Chaulnes (Mem. de VAcademic, 1755, p. 141) for the case in which they are unlike. In this experiment a plano-convex lens was employed. Each face in succession, after having been tarnished, was turned towards the incident light. It appears from a passage at the end of Newton's twelfth Observation that he had himself made experiments of a similar nature, the results of which however are not described.